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Properties

Label 2736.3.bo
Level $2736$
Weight $3$
Character orbit 2736.bo
Rep. character $\chi_{2736}(1969,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $476$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.bo (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2736, [\chi])\).

Total New Old
Modular forms 1944 484 1460
Cusp forms 1896 476 1420
Eisenstein series 48 8 40

Trace form

\( 476 q + 3 q^{3} + q^{5} + 2 q^{7} + 7 q^{9} + O(q^{10}) \) \( 476 q + 3 q^{3} + q^{5} + 2 q^{7} + 7 q^{9} + 2 q^{11} + 3 q^{15} - 26 q^{17} + 4 q^{19} + 24 q^{21} + 2 q^{23} - 1149 q^{25} - 3 q^{29} + 72 q^{31} + 24 q^{33} - 23 q^{35} - 5 q^{39} + 33 q^{41} + 98 q^{43} - 29 q^{45} - q^{47} - 1584 q^{49} + 3 q^{51} - 6 q^{53} - 23 q^{55} + 13 q^{57} + 3 q^{59} + q^{61} - 25 q^{63} + 6 q^{65} - 27 q^{69} + 6 q^{71} + 10 q^{73} - 534 q^{75} + 194 q^{77} - 217 q^{81} + 2 q^{83} + 98 q^{85} - 117 q^{87} - 6 q^{89} - 429 q^{91} - 19 q^{93} + 167 q^{95} - 97 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1368, [\chi])\)\(^{\oplus 2}\)